In a certain code language, the word "ARMS" is written as "5467" and the word "LIAR" is written as "1254". Using the same letter to digit substitutions, how is the word "SMALL" written in that code language?

Introduction:
This question tests your ability to decode and apply a simple substitution cipher in which each letter is replaced by a specific digit. We are given coded forms for two words, "ARMS" and "LIAR", and must determine the code for a third word, "SMALL". The core skill here is to extract consistent letter to digit mappings and then reuse them in the required word without contradiction.

Given Data / Assumptions:
The word "ARMS" is coded as "5467" and the word "LIAR" is coded as "1254". Each letter is assumed to map to exactly one digit, and the same letter always has the same code wherever it appears. We also assume that there is no position based trick and that the code is a straightforward one to one substitution from letters to digits.

Concept / Approach:
To solve this, we must first determine the digit corresponding to each letter by aligning letters with their positions in the code. Once we know the mappings for the letters S, M, A, and L, we can write the complete code for "SMALL". The idea is to build a mapping table such as A to a specific digit, R to another, and so on, and then read off the encoded version of the new word.

Step-by-Step Solution:
Step 1: Consider "ARMS" coded as "5467". Match letters and digits position wise: A corresponds to 5, R to 4, M to 6, and S to 7.Step 2: Now consider "LIAR" coded as "1254". Matching the letters: L corresponds to 1, I to 2, A to 5, and R to 4.Step 3: From these two words we have the following consistent mappings: A = 5, R = 4, M = 6, S = 7, L = 1, I = 2. All mappings agree where letters repeat.Step 4: We now need the code for the word "SMALL". The letters in order are S, M, A, L, L.Step 5: Using the mappings: S = 7, M = 6, A = 5, and L = 1.Step 6: Therefore, "SMALL" becomes the string of digits 7 6 5 1 1, that is, 76511.

Verification / Alternative check:
We can double check by inserting each individual mapping back into the earlier examples. Substituting A = 5, R = 4, M = 6, S = 7 in "ARMS" regenerates "5467" and substituting L = 1, I = 2, A = 5, R = 4 in "LIAR" regenerates "1254". Since there is no contradiction, the mapping is valid, and our encoding of "SMALL" is reliable.

Why Other Options Are Wrong:
The option 76521 assigns the last two letters L and L to 2 and 1, which conflicts with the mapping L = 1 established from "LIAR". The option 76512 also breaks the requirement that both L letters have code 1. The option 76544 would require L to map to 4, but that digit is already fixed for R. The option 76514 similarly introduces inconsistent digit assignments for L.

Common Pitfalls:
A common mistake is to attempt to guess the final code without carefully listing the mappings, which can lead to mixing up digits for letters that look similar or appear multiple times. Another pitfall is forgetting that the same letter must always have the same code, which immediately invalidates many tempting but incorrect options.

Final Answer:
The word "SMALL" is written in the code language as 76511.